2000/11/27 by Z. Burda, Zdzislaw Burda, Pawel Sawicki
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Excited state #Fermion #Generalization #Ground state #Limit (mathematics) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum system #State (computer science) #cond-mat #hep-lat
paper · pdf · doi:10.1088/0305-4470/34/19/301
published as J.Phys.A34:3947-3956,2001 · 14 pages, Latex + 4 eps figures
arxiv created 2000/11/27 · openalex publication_date 2001/05/02 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss a new numerical method for the determination of excited states of a quantum system using a generalization of the Feynman-Kac formula. The method relies on introducing an ensemble of non-interacting identical systems with a fermionic statistics imposed on the systems as a whole, and on determining the ground state of this fermionic ensemble by taking the long-time limit of the Euclidean kernel. Due to the exclusion principle, the ground state of an n -system ensemble is realized by the set of individual systems occupying successively the n lowest states, all of which can therefore be sampled in this way. To demonstrate how the method works, we consider a one-dimensional oscillator and a chain of harmonically coupled particles.